What are the values of cos α and tan α, if: sinα= 40/41

The answer to your question is:

cos α = 9/ 41

tan α = 40/9

Step-by-step explanation:

Data

cos α = ?

tan α = ?

sin α = 40/41

Process

sin Ф  = opposite side / hypotenuse

then, if sin α = 40/41,

opposite side = 40

hypotenuse = 41

Pythagorean theorem

                                       c² = a² + b²

                                      41² = 40² + b²

                                      b² = 41² - 40²

                                      b² = 1681 - 1600

                                      b² = 81

                                      b = 9

adjacent side = 9

Now,

cosine Ф = adjacent side / hypotenuse

cos α = 9/ 41

tangent Ф = opposite side / adjacent side

tan α = 40/9